## O

SautP Pw large positive vorticity small positive vorticfty zero vorticity smaii negative vortieiy large negative vorticity anticlockwise rotation clockwise rotation

Earth's axis of rotation la)

Figure 4.7 (a) Schematic diagram to show the variation of planetary vorticity with latitude. The blue arrows represent the component of the Earth's rotation about a local vertical axis (viewed from above) at different latitudes.

(b) Diagram to show the derivation of the expression for the planetary vorticity of a fluid parcel on the surface of the Earth at latitude <j). (For use with Question 4.3(a).)

*This is easiest to imagine for a location close to one of the poles - you can try it yourself by marking a cross on a globe, and turning it slowly while keeping your viewpoint directly above the cross.

angular velocity = II Earth's axis of rotation angular velocity = II

angular velocity - Í1 simt> planetary vorticity =

While the linear eastward velocity of the Earth's surface decreases wilh latitude, its angular velocity about a local vertical axis increases with latitude (Figure 4.7At the poles, the angular velocity of the surface of the Earth is simply £2 (= 7.29 X Kr-V (cf. Section 3.2)), At increasingly lower latitudes, it is a smaller and smaller proportion of £2: the bigger the angle between the Earth's axis of rotation and the local vertical axis, the smaller the angular velocity of the surface of the Earth about this local vertical axis. Al the Equator, where a vertical axis is at right angles to the axis of rotation of the Earth, the angular velocity of the surface is zero. In general, ihe angular velocity of the surface of the Earih about a vertical axis at latitude d> is given by £2 sin <J> (Figure 4.7(b)).

If the surface of the Earth at latitude <D has an angular velocity of Q sin 0. so too does any object or parcel of air or water on the Earth at that latitude. In other words, any parcel of fluid on the surface of the Earth shares ihe component of the Earth's angular rotation appropriate to that latitude.

The vorticily of a parcel of 11 uid is defined mathematically to be equal to twice its angular velocity.